The visualization of the tumor vascularization using micro computed tomography

The Visualization of the Tumor Vascularization using Micro Computed Tomography

Inauguraldissertation zur

Erlangung der W¨urde eines Doktors der Philosophie vorgelegt der

Philosophisch-Naturwissenschaftlichen Fakult¨at der Universit¨at Basel

von

Sabrina Lang aus Kiel, Deutschland

Basel, 2012

Genehmigt von der Philosophisch-Naturwissenschaftlichen Fakult¨at auf Antrag von:

Prof. Dr. Bert M¨uller, Fakult¨atsverantwortlicher Prof. Dr. Thomas Jung, Co-Referent

Basel, den 13. Dezember 2011

Prof. Dr. Martin Spiess Dekan

Contents

Summary 1

Zusammenfassung 3

1 Introduction 5

1.1 Micro Computed Tomography to Visualize Tumor Vessel Trees . . . 5

1.2 Quantitative Evaluation of SRµCT Data from Tumor . . . 7

1.3 Necessary Procedures to Obtain Vector-based Vessel Trees . . . 8

1.3.1 Specimen preparation . . . 8

1.3.2 Data Acquisition using SRµCT . . . 9

1.3.3 Image Processing . . . 9

2 Visualization of Tumor Vessels using Synchrotron Radiation-based Micro Computed Tomography 11 2.1 Introduction . . . 11

2.2 Materials and Methods . . . 11

2.3 Results and Discussion . . . 12

3 Global and Local Hard X-ray Tomography of a Centimeter-sized Tumor Vessel Tree 15 3.1 Introduction . . . 15

3.2 Methods and Materials . . . 16

3.2.1 Specimen Preparation . . . 16

3.2.2 Synchrotron Radiation-based Micro Computed Tomography . . . 17

3.2.3 Data Analysis . . . 17

3.3 Results . . . 19

3.3.1 Differences between Global and Local Radiographs . . . 19

3.3.2 Analysis of the Flat-field Images . . . 22

3.3.3 The Absorption Histograms of Global and Local Tomography Slices . . 23

3.3.4 The Absorption Histograms of Global and Local Tomograms . . . 23

3.3.5 Correcting Local Tomograms using Histogram Matching . . . 23

3.3.6 Extending Local Sinograms by Less Detailed Global Data . . . 28

3.3.7 Empirical Cupping Correction . . . 28

3.3.8 Tumor Vessel System . . . 29

3.4 Discussion . . . 29

3.5 Conclusion . . . 34

4 Comparing Grating-based and Propagation-based Phase-contrast Computed

Tomography for Soft Tissue Imaging 37

4.1 Introduction . . . 37

4.2 Material and Methods . . . 39

4.2.1 Specimen preparation . . . 39

4.2.2 Data acquisition and processing . . . 39

4.2.3 Tomographic reconstruction . . . 44

4.2.4 Comparative analysis and quality assessment . . . 45

4.3 Results . . . 48

4.4 Discussion . . . 48

4.5 Conclusion . . . 54

5 Morphological assessment of the vessel trees in cancerous and healthy tis- sues using synchrotron radiation-based micro computed tomography 65 5.1 Introduction . . . 65

5.2 Material and Methods . . . 66

5.3 Image Analysis . . . 67

5.4 Results . . . 69

5.5 Discussion . . . 72

5.6 Conclusion . . . 74

6 Conclusion 77

Acknowledgments 88

Curriculum Vitae 90

Summary

Cancer has been one of the most serious diseases and according to the world health organiza- tion (WHO) the total number of deaths due to cancer (7.6 million worldwide) will globally in- crease in future to 13.1 million deaths. Tumor-growth is strongly related to the neo-formation of blood vessels (angiogenesis), since the vessels provide the cancerous tissue with the neces- sary nutrients and oxygen. For this reason in this study 3D high resolution visualization and parametrization of tumor vessels down to capillary size was carried out. 3D datasets were acquired using synchrotron radiation-based micro computed tomography (SRµCT) which pro- vided sufficient spatial resolution to make also the smallest vessels down to 4µm visible. The contrast in the image is defined by the degree of X-ray attenuation/absorption in the spec- imen. Because absorption coefficients did not differ significantly between different kinds of soft biological tissue, contrast enhancement of the specimens was needed to obtain sufficient contrast in the tomograms. Contrast enhancement was done either by blood vessel staining using a contrast agent (see Chapter 2) or by generating corrosion casts of the vessels (see Chapters 2 and 4). Alternatively, phase contrast based SRµCT was used which allowed the vessel tree visualization without any contrast enhancement (see Chapters 3 and 4). This technique measures the phase shift of the photon beam induced by a tumor. The sensitivity was shown to be 25 times higher in comparison to the absorption contrast based data.

By staining the tumor vascularization as seen in Chapter 2, characteristics of the tumor vessel morphology could be revealed. According to the vessel shape and the vessel density it was possible to identify the interface between the tumor and the healthy tissue. Vessels in can- cerous tissue appeared strongly twisted. Additionally, several regions were found in tumors where the contrast agent leaked out from the cancerous vessels presumably due to damages of the vessel walls within the cancerous tissue. Vessel-free regions could be observed which gave evidence of necrosis in the tumor.

Most of the tumors exceeded the field of view, i.e. they do not fit the image of the camera, when using high resolution optics to reveal the smallest vessels in the 3D dataset. Local tomography of a tumor cast was carried out to allow high resolution imaging of a region of interest. Because of the interest in the morphology of the whole tumor the local tomography data was compared to the less resolution global SRµCT data. It was shown that the absorp- tion coefficients in the locally acquired data differed significantly from the ones of the global datasets. These differences are caused most probably by the non-locality in the filtered back- projection calculation which is needed to generate tomograms out of the radiographs. These non-locality artifacts caused the absorption coefficients in the tomographic slices to shift to higher values for increasing distances of the pixels to the rotation center. For this reason this effect is also called ’cupping artifact’. Additionally the high resolution images were affected by edge enhancement due to the coherence of the X-ray beam which caused the peaks in the

image histogram to appear more broadened.

One correction method, de-cupping method, empirically post-corrected the cupping artifacts in the local tomograms using the global data as reference. In another correction method the origination of these artifacts was prevented by extending the local sinograms using the less detailed global ones. Mathematically a sinogram is the radon transform of a tomographic slice [1]. It can easily be constructed using the corresponding radiographs acquired at dif- ferent rotation aFngles. While the sinogram extension method proved better correction of the total µ-shift (90%), the de-cupping method was more suitable to correct the histogram broadening (78%). By matching the global and local histograms in the projections the peak broadening caused by edge enhancement could be reduced by 41%.

An alternative method to measure the blood vessels using SRµCT is based on the measure- ment of the X-Ray phase shift instead of the X-ray absorption when transmitting through the specimen. The quality of two such phase contrast based SRµCT methods (grating and propagation-based) was analyzed in Chapter 4, using the contrast-to-noise-ratio, the spatial resolution and the presence of artifacts. For the measured tumor tissue the holotomography technique provided better spatial resolution (SR = 8 µm) in comparison to the grating in- terferometry (SR = 24 µm). The contrast to noise ratio however is much better in grating interferometry (CNR = 57) than in holotomography (CNR = 11).

For further studies the data obtained by holotomography was used, as it provided the visu- alization of the smallest vessels despite the reduced contrast. Together with the absorption contrast based vessel cast of healthy and cancerous tissue the tumor, measured with holoto- mography, were analyzed according to their vessel parameters. Skeletonization and vector- ization of the voxel based data allowed an easier extraction of the characteristic parameters.

The calculations revealed a mean vessel diameter of 8.8 ± 4.2 µm and a tortuosity value of 0.18± 0.19 rad for all vessels in the healthy corrosion cast. The cancerous vessels showed a mean diameter of 5.4 ± 5.5 µm and a mean tortuosity value of 0.24 ± 0.25 rad. While the value for the vessel diameter showed differences between healthy and cancerous tissue, the tortuosity was more or less equal for both tissues. The quantification of vessel trees using SRµCT data belongs to the vital steps in understanding of tumor formation and growth and in developing strategies against the disease.

Zusammenfassung

Krebsleiden z¨ahlen zu den lebensbedrohlichsten Krankheiten der modernen Welt und laut Aussage der Weltgesundheitsorganisation (WHO) wird die Anzahl von Krebserkrankungen auch in Zukunft weiter ansteigen. Um Fortschritte in der medizinischen Behandlung von Krebspatienten zu erzielen, ist die Erforschung des Tumorwachstums grundlegend. Die Expan- sion eines Geschwulstes wird duch die Angiogenese vorangetrieben, da die Bildung von neuen Blutgef¨assen die Versorgung des Krebsgewebes mit Sauerstoff und den n¨otigen N¨ahrstoffen gew¨ahrleistet. Aus diesem Grund besch¨aftigt sich diese Arbeit mit der Visualisierung und Analyse von Blutgef¨assen in Tumoren.

Zur 3-D-Darstellung der Blutgef¨asse wurde Mikro-Computertomographie an Synchrotron- strahlungsquellen (SRµCT) verwendet. Diese bildgebende Technik liefert hochaufgel¨oste Auf- nahmen, die auch kleinste Blutgef¨asse mit einem Durchmesser von 4µm sichtbar machen. Der Bildkontrast wird dabei durch die Absorption der R¨ontgenstrahlung in der Probe bestimmt.

Bei Weichgewebe sind die Unterschiede in den Absorptionswerten jedoch zu gering, um die Blutgef¨asse vom umliegenden Gewebe zu unterscheiden. Aus diesem Grund wurden in der vorliegenden Arbeit kontrastverst¨arkende Massnahmen durchgef¨uhrt.

In Kapitel 2 wird beschrieben wie ausreichender Kontrast durch die F¨arbung der Gef¨asse mit Hilfe eines Kontrastmittels herbeigef¨uhrt wurde, so dass deren Morphologie erkennbar wurde. Die damit gewonnenen Daten machten es m¨oglich, gesundes von krankem Gewebe zu unterscheiden. Erkranktes Gewebe zeigte in den CT-Bildern vermehrt spiralf¨ormige Blut- gef¨asse und man konnte erkennen, dass das F¨arbungsmittel an einigen Stellen ausgelaufen sein musste. Dies l¨asst auf eine Nekrotisierung der Blutgef¨asse schliessen, welche ausserdem zur Folge hatte, dass grosse Bereiche des Tumores ¨uberhaupt keine Blutgef¨asse vorwiesen.

Da viele der untersuchten Tumore gr¨osser als das durch den Detektor vorgegebene Sicht- feld waren, wurden sowohl lokale SRµCT-Messungen eines ausgew¨ahlten Bereiches als auch globale SRµCT-Messungen des gesamten Tumors, aber mit einer schw¨acheren Aufl¨osung, durchgef¨uhrt (Kapitel 3). Um einen gen¨ugend hohen Kontrast zu erhalten, wurde f¨ur den Vergleich der globalen und lokalen Messungen ein Blutgef¨assabguss aus Polymer erstellt. Es stellte sich heraus, dass sich die Absorptionswerte in den lokalen Tomogrammen von denen in den globalen Tomogrammen unterschieden. Diese Unterschiede k?nnen auf die Nicht-Lokalit¨at der gefilterten R¨uckprojektion zur¨uckgef¨uhrt werden, ein Verfahren, das die Tomogramme aus den Projektionen errechnet. Diese verursachte eine ansteigende Verschiebung der Ab- sorptionskoeffizienten zu gr¨osseren Werten. Zus¨atzlich f¨uhrte die Koh¨arenz der Strahlung bei der hohen Aufl¨osung in den lokalen Bildern zu einer vermehrten Kantenverst¨arkung, so dass die Peaks in den Histogrammen breiter wurden. Da die Absorptionswerte in den glob- alen Tomogrammen den wahren Absorptionswerten der Probe am n¨achsten kommen, wurden die Werte in den lokalen Tomogrammen denen der globalen Tomogramme angepasst. Um

die Artefakte der nicht-Lokalit¨at zu korrigieren, wurden diese zum einen empirisch bestimmt und aus den Bildern entfernt. In einer zweiten Methode wurde die Bildung dieser Artefakte umgangen, indem vor der Rekonstruktion die fehlenden Bereiche in den lokalen Projektio- nen durch die entsprechenden in den globalen Projektionen ersetzt wurden. W¨ahrend die Artefakt-reduzierende Methode die gr¨osstm¨ogliche Korrektur der nicht-linearen Verschiebung der Absorptionskoeffizienten lieferte (78%), wurde die bestm¨ogliche Korrektur der totalen Ver- schiebung mit Hilfe der Projektionserweiterungen zu 90% herbeigef¨uhrt. Die durch Kanten- verst¨arkung verbreiterten Peaks konnte man am besten korrigieren, indem man die Grauwert- bereiche in den Histogrammen der Projektionen vor der Rekonstruktion aneinander anpasste (41%).

Eine alternative Methode zur Bildgebung der Blutgef¨asse mit Hilfe von SRµCT basiert auf der Messung der durch die Probe verursachten Phasenverschiebung der R¨ontgenstrahlung. Da es verschiedene Methoden in der Phasenkontrast-basiertenµCT gibt, wurden in Kapitel 4 die Qualit¨atsunterschiede zweier solcher Methoden (Gitterinterferometrie und Holotomographie) untersucht. Die Qualit¨at wurde unter anderem anhand der r¨aumlichen Aufl¨osung und des Kontrast-zu-Rausch-Verh¨altnisses definiert. Dabei lag die Gitterinterferometrie mit einem f¨unffach h¨oheren Kontrast-zu-Rausch-Verh¨altnis gegen¨uber der Holotomographie im Vorteil.

Die Holotomographie erm¨oglicht im Gegensatz dazu eine dreimal bessere Aufl¨osung. Obwohl diese Methode einen schw¨acheren Kontrast vorweist, wurde sie f¨ur weitergehende Studien verwendet, da sie die M¨oglichkeit bot auch die kleinsten Blutgef¨asse darstellten zu k¨onnen.

Zusammen mit den absorptionsbasierten Tomogrammen der Blutgef¨assabg¨usse, sowohl von gesundem als auch krebskrankem Gewebe, wurden die Holotomographiedaten verwendet, um die Gef¨assparameter zu bestimmen. Dazu wurden die dreidimensionalen voxelbasierten Daten skelettiert und anschliessend vektorisiert, was die Auswertung erleichterte. Die Berech- nungen f¨ur gesundes Gewebe ergaben einen mittleren Gef¨assdurchmesser von 8.8 ± 4.2 µm und ein Ausmass der Gef¨asswindungen von 0.18 ± 0.19 rad. Tumore zeigten dagegen einen Gef¨assdurchmesser von 5.4±5.5µm und eine Ausmass der Gef¨asswindungen von 0.24±0.25 rad. W¨ahrend die Werte des Durchmessers sichtbare Unterschiede zwischen dem gesunden und dem kranken Gewebe aufweisen, sind bei dem Ausmass der Gef¨asswindungen im Rahmen der Messungen keine Unterschiede erkennbar. Die Parametrisierung der Blutgef¨asse mit Hilfe der SRµCT geh¨ort zu den vielversprechenden Methoden um die Tumorbildung zu untersuchen.

Chapter 1

Introduction

1.1 Micro Computed Tomography to Visualize Tumor Vessel Trees

Cancer is the second most frequent cause of death in society, although the therapeutic strate- gies are constantly refined [2]. The formation of new blood vessels, angiogenesis [3, 4], is a crucial step for the survival and metastasis formation of malignant tumors [5]. This is be- cause, like normal tissues, tumors require an adequate supply of oxygen, metabolites and an effective way to remove waste products [6]. Although novel therapeutic strategies attempt- ing to inhibit this step are being developed, the biological regulation of this process is still largely unknown. A computer simulation model should help to investigate tumor formation and growth, and finally contribute to the development of treatment strategies like optimizing dose delivery during radiation therapy or systematic selection of anti-angiogeonic drugs and improve the insight of the underlying mechanisms [7, 8]. To make sure that the computed results agree with tumors, one has to compare them with measured data. The visualization of the 3D vessel network is therefore crucial for studying the physiological processes related to angiogenesis and vascular diseases.

A most common way to analyze the morphology of blood vessel systems is the use of histol- ogy [9]. Unfortunately 3D characterization via serial sectioning is very tedious and time con- suming [10]. Also, the sectioning damages the biological material [11]. Promising microscopy techniques, such as two photon microscopy, gives the opportunity of screening localizedin vivo physiological signals [12, 13]. Unfortunately, multi-photon laser microscopy is still limited to about 200 µm depth and a restricted field of view. Other methods like scanning electron microscopy [14]in situ appear really accurate but are restricted to the investigation of several 100 µm, due to the finite penetration ability. Magnetic resonance imaging allows in vivo visualization of the vascular network of the whole tumor without causing damage [15, 16].

This technique achieves a resolution in the range of a few 100 µm. However, most of the vessel diameters lie between 3 and 10µm (50% in the cerebral cortex), therefore micrometer resolution is necessary to visualize the smallest capillaries [17, 18]. Micro Computed Tomog- raphy (µCT) is a 3D imaging technique which provides micrometer resolution or by adding X-ray optics even in the nanometer resolution. µCT works like conventional clinical CT where the intensity changes of x-ray photon beams are detected after transmission through the ob- ject. The source of the x-rays can be a cone-beam emitting x-ray tube (laboratory source).

Another x-ray source, synchrotron radiation, has several advantages over the conventional x-ray tube. Using synchrotron x-ray sources one gets a coherent and very bright photon beam [19, 20]. The increased photon flux results in a reduced exposure time which causes a reduction in the data acquisition. A reduced experimental time-scale lowers problems due to time dependent mechanical instabilities like shrinkages and expansions of soft biological tissue [20]. Furthermore the synchrotron radiation source can provide a monochromatic beam which avoids beam-hardening artifacts.

Although the contrast is visibly better in Synchrotron Radiation-basedµCT (SRµCT), one is still not able to make the vessels visible. Conventional absorption basedµCT is based on the attenuation of the light transmitting through the specimen.The attenuation can be described by the Beer-Lambert law:

I

I₀ =e^−µd (1.1)

I₀ and I are the intensities of the incident and transmitted radiation respectively. The spec- imen thickness is given by d. The absorption coefficient µ does not differ strongly between different kinds of soft biological tissue. In tumors it is therefore difficult to distinguish between the vessels and their surroundings. To be able to see vessels in conventional SRµCT one has therefore to increase their contrast. There are contrast enhancing preparation methods, which were successfully applied in imaging the vascular network of the different organs. The most common way of increasing the contrast is the staining method [17, 21–23], where a contrast agent is injected into the vessels which does not penetrate through the vessel walls.

Another promising method is corrosion casting, where a cast agent is perfused in the vascular network of an animal [24–26]. After resin curing (1-2 d), the soft tissue is macerated, followed by decalcification, each for 24 hours. ForµCT the casts can be immersed in osmium tetroxide (OsO4) for several days to increase the attenuation of the light in the specimen.

AnotherµCT technique, where the vessels can be visualized without any contrast enhancing preparations, is the phase contrast based µCT [27–33]. In phased contrast based µCT the phase shift of the transmitting beam is determined instead of the attenuation which more sensitive to structural differences within an object. The phase shift is related to the real decrementδof the refractive indexn= 1 +iβ−δ. βis related to the absorption coefficientµ.

Due to its high sensitivity also differences in soft tissue can also be visualized. There are sev- eral techniques that have been implemented to visualize variations in the phase. One method to induce the phase shift is the propagation basedµCT [34]. Its main advantage lies in the rather simple experimental setup [35]. No specialized optical elements are required in order to render phase shifts visible as intensity variations, because phase contrast may be achieved by the simple free-space propagation [36]. To obtain the phase shift, projections are acquired at different sample-to-detector distances. The quantity obtained by this measurement is related to the Laplacian (the second derivative) of the refractive index [37]. Although the experi- mental setup is easy to handle this is not the case for the retrieval of the phase information from acquired data. The phase shift can be obtained by resolving the relationship between the specimen induced phase shift and the contrast recorded at a sample-to-detector distance.

There are different approximation techniques to solve this problem. A mixed approach of the contrast transfer function (CTF) and the transport of intensity equation (TIE) can be used to obatin the phase information in the images. The different methods depend on the compositions of the specimen. These methods need data from at least three different sample-

to-detector distances. However, taking a reduced quality into account, one can obtain phase information using the Paganin method where only single-distance data are necessary [36].

Another phase imaging method in tomography is grating interferometry [27, 29, 29, 31, 38].

This method takes advantage of two gratings. One is the phase grating which separates the incoming beam in the first order and generates a self-image at a defined distance. A second grating (amplitude grating) is placed in the plane of the self image which serves as an intensity mask [39]. The differential phase shift is calculated by comparing the intensity distribution without any perturbations with that of an object placed in front of the grating.

Although the experimental setup is more complex and needs more mechanical stability in comparison to in-line methods [40], phase retrieval can easily be determined using the phase stepping method [41]. In contrast to the propagation based technique the specimen has to be measured in a medium which offers a similar refraction index to the specimen itself. Tumor samples usually are measured inside a water tank to prevent phase wrapping artifacts.

The 3D information can be calculated from absorption and/or phase contrast basedµCT using the filtered back-projection algorithm [1]. The vessels can be isolated from the tomograms using an appropriate segmentation method. But even if the volumetric data allows for an easy vessel tree segmentation, the data have to be translated to vector-based representations to allow the direct comparison with the related computer simulations. From the vectorized data one can easily determine different vessel parameters like the vessel radii and length or the number of bifurcations, which are relevant to define the vessel morphology. From the obtained parameters one is not only able to define differences between healthy and cancerous tissue but can also help to validate and improve computer programs simulating the tumor neo-vascularization for a better insight into tumor growth.

The challenge of the tumor vessel analysis down to the capillary size lies 3D imaging including appropriate spatial and density resolution. The GB sized data is needed to be segmented and parametrized properly afterwards.

1.2 Quantitative Evaluation of SRµCT Data from Tumor

The biggest obstacle in the visualization of the vascular networks lies in the low contrast between the vessels and the surrounding tissue, using conventional absorption µCT. Differ- ent specimen preparation methods andµCT techniques were carried out to make the vessels visible inside the tumor tissue. In this thesis three different kinds of imaging techniques are proposed to overcome the problem of insufficient contrast.

In Chapter 2 the effectiveness of the contrast enhancing staining technique is presented. For that purpose a closer look at the tumor vessel morphology is taken.

Although the spatial resolution in SRµCT was sufficient large to make the capillaries visible, limitations can occur depending on the size of the specimen. Because of the limited detector size and the cubically increasing amount of image data produced in moving to smaller voxel sizes, there is a trade-off between resolution and volume that can be acquired in a single scan.

The maximum pixel size, which is enough to reveal the smallest capillaries, is approximately 1.5µm. As most of the available detectors at synchrotron radiation beamlines have a range of (2048x2048) pixels, the field of view (FOV) is limited to approximately 3 mm. Tumors differ strongly in shape and size. The limitation in the FOV is therefore a limitation in the analysis of the tumor vessels. Cutting the tumor to the appropriate size of the FOV would

be an unpredictable invasion in the tumor morphology. µCT offers the possibility for region- of-interest (ROI) or local imaging of a specimen which exceeds the FOV. Local tomography however is inherent with diverse artifacts which affect the density distribution and therefore the possibility to segment the vessel tree appropriately.

In Chapter 3, high-resolution local tomography data of the tumor cats were compared with the one obtained by global tomography, where the specimen, in contrary to local tomography, fits the whole field of view of the camera [25]. In order to adapt the absorption values obtained from the two approaches, the de-cupping, sinogram extension and histogram matching was compared. The question arised which of these approaches provides the best results.

Absorption basedµCT images require sufficient contrast to make vessels visible in the tomo- grams. As contrast enhancement mechanisms in absorption contrastµCT may cause changes in the morphology of the vascularization, an alternative is proposed in Chapter 4. ThisµCT technique is based on the phase contrast, i.e., measures the phase shift of an incoming beam transmitting through an object of interest. Since phase contrast-basedµCT is more sensitive than absorption contrast, it is an appropriate method for the imaging of soft biological tissue.

There are different techniques to reveal the phase shift indirectly. The prominent methods, the grating interferometer and the propagation based tomography, which imply the Paganin method and holotomography, are used in the study presented in Chapter 4. The study exam- ines the image quality of the proposed methods in the visualization of soft biological tissue, defined by the spatial resolution, the contrast to noise ratio and the existence of artifacts.

Additionally an alternative specimen, here a rat-heart, was included to give a broader spec- trum of examples for soft tissue and the found results.

The morphometric analysis of the visualized tumor vessels is presented in Chapter 5. Vessel parameters like the vessel density, the vessel diameter and the bifurcation density are an- alyzed to define the characteristics common and unique to tumor and healthy tissue. The multi-modal data (absorption contrastµCT of corrosion casts and holotomography) give ev- idence of the effectiveness to analyze the vascular structures of tumors.

The final conclusions can be found in Chapter 6.

1.3 Necessary Procedures to Obtain Vector-based Vessel Trees

1.3.1 Specimen preparation

The measured tumor samples were obtained from the Institute of Biomedical Engineering at ETH and University of Zurich. After the in vivo experiments [42], when the tumor reached a size which caused sufferings to the animal or led to a preferred size for following experiments, the mice with a weight of approximately 25 g were euthanized by an intraperitoneal injection of 350 ml Ketamine/Xylazine, the quantity varied depending on the individual weight of the mouse. Depending on the imaging technique used, the tumor, was isolated and stabilized on a sample holder to prevent movement of the specimen during data acquisition.

Staining : The contrast agent was a suspension of nanometer-size barium sulfate (BaSO₄) and physiological solution with a concentration of 80 g/l. The suspension was filtered (pore size±1µm, BD Falcon, USA) to obtain particles with dimensions less than the diameters of the smallest vessels. Before injection, the suspension was homogenized using the ultrasonic bath Sonorex Digital 10P, Bandelin at a temperature of 37^◦C for a period of 10 min. After

anesthesia the animal was perfused with 250 ml heparin to avoid thrombosis. Finally, 10 ml barium sulfate suspension was injected via the left ventricle of the heart applying the peristaltic pump (Watson Marlow 101 U/R) as described in [43]. The barium sulfate solution was mixed with ink to optically follow that the staining of the whole vascular system was complete. Staining was judged as complete when the spleen became colored.

Corrosion Cast: Before application the resin was mixed with an hardener. As with the staining method the mice were perfused with 250 ml heparin to avoid thrombosis. Thereafter the polymer was injected with a peristaltic pump. Also here the injection could be traced using blue ink as a marker. The polymer hardening took 2-3 days then the corrosion of the soft and hard tissue was carried out using formic acid. After 5-7 days the mouse body was dissolved by the acid and only the polymer in form of the mural vascularization remained.

The tumor vessels were cut from the cast and coated with osmium tetroxyd (OsO₄) to provide better contrast in the tomograms.

Phase Contrast Imaging: Since no contrast enhancing was necessary after extraction the tumor was only fixed in 4-5% para-formealdehyde (PFA) to prevent the tissue from damages due to decomposition and transferred into polymer containers for the imaging using SRµCT.

1.3.2 Data Acquisition using SRµCT

The SRµCT-measurements were performed at the beamline TOMCAT (SLS at PSI, Villigen, Switzerland) and BW2 (HASYLAB at DESY, Germany) for absorption based µCT and at the beamline ID19 (ESRF, Grenoble, France) for the phase contrast basedµCT. The beam- lines offered the experimental equipment and software for the µCT measurements. As the available experimental equipment for the grating interferometer offered only the possibility to carry out medium resolution tomography, it was necessary to build a high-resolution (spa- tial resolution is better than 5 µm) grating interferometer at the beamline ID19. For that purpose the construction of the setup and the experimental conditions were developed. The construction also required the application of the motors running by the available software to control the gratings. For the in-line tomography experiments no adoptions were required as no special setting is needed and the software for the data acquisition was already provided by the beamline. In the case of the specimen to be measured in PFA one had to take into account that bubble development could cause artifacts in the tomograms due to specimen movements or phase wrapping in phase contrastµCT. To reduce the bubble development the specimens were therefore degassed in a vacuum chamber at around 10 mbar to remove the dissolved air in the liquid. After data acquisition the tomograms were generated by fully automatic re- construction tools based on filtered back projection [1]. Each synchrotron beamline provided a corresponding reconstruction tool for this purpose. Before the reconstruction of the phase contrast basedµCT data, one had to retrieve the phase shift information of the raw data.

1.3.3 Image Processing

To obtain the phase information from the acquired images of the grating interferometry and the propagation based tomography, phase retrieval processings are necessary. For the different technFAiques adequate software was provided at ESRF (Computer code in IDL (ITT Visual Information Solutions, Boulder, Colorado, USA), for grating interferometry [44], ANKAphase for Paganin [45] and a phase retrieval algorithm for holotomography implemented in GNU

Octave version 2.1.73 [37]). While the tools for the grating interferometry and the Paganin are fully automatic, the holotomographic reconstruction needed pre-processing, for example, the alignment of the one-angle projections acquired at different sample-to-detector distances.

For data comparison of specimens which were measured under different imaging conditions, registration was required. For the comparison of two projections or two single tomograms 2D registration was performed with a registration algorithm implemented in Matlab. In case of 3D data registration the tool offered by [46] was used.

For the visualization of the vessels the voxels which are part of the vessels had to be segmented.

In the absorption contrast based µCT data of the stained specimen and the corrosion cast this was easily be done by defining an appropriate intensity-based threshold. Quantitatively this threshold was obtained by using the Otsu method or by finding the intersection points between the Gaussians of the vessels and the surrounding objects in the histogram. This kind of segmentation is very effective as long as the object of interest is presented by distinguishable Gaussians in the histogram. As soon as the histogram peaks of two different objects merge together this method can not be used to segment the corresponding objects separately. This is the case in the phase contrast based tomograms, where the intensity values of the vessel are shared with other objects in the surrounding tissue. Setting a threshold would segment both objects, therefore a feature-based segmentation was needed. In case of the vessels which was approximated as tubes which differ in length and diameter the Frangi filter was applied.

The Frangi filter is based on the advanced line detection tool described in [47] and [48].

For the analysis of the vessel characteristics a vectorization tool was developed (see Chapter 5) which allows extraction of vessel parameters and additionally decreases the data size by approximately 50%. The vectorization tool needs two formats for each dataset. One is the segmented and binarized 3D dataset, the other one contains its centerline. To obtain the centerline of the 3D image a skeletonization tool offered by [49] was used.

For the 3D visualization of the blood vessels the software VG Studio Max 2.0 (Volume Graph- ics, Heidelberg, Germany) was applied. Thresholds and colors were manually selected to elucidate the features of interest.

Chapter 2

Visualization of Tumor Vessels

using Synchrotron Radiation-based Micro Computed Tomography

2.1 Introduction

The vascular structure of tumors differs from that of healthy tissue. To understand the formation of cancerous tissue, the vascular network of tumors should be uncovered down to the capillary level. Standard synchrotron radiation-based micro computed tomography (SRµCT) in absorption contrast mode provides the necessary micrometer resolution [17] even for centimeter-sized tumors [21]. The visualization of a vessel tree, however, also requires sufficient contrast. Because the tissue consists mainly of water and low absorbing species, SRµCT does not lead to significant X-ray absorption differences between vessels and sur- rounding tissue. So, the successful application of absorption contrast tomography requires dedicated tissue preparation procedures including embedding [22] and corrosion casting [23].

The more common procedure is the use of staining materials such as the incorporation of barium sulfate into the vessels [10, 11, 17, 21, 25].

2.2 Materials and Methods

The present study is based on the injection of a barium sulfate suspension with a grain size of 0.5 to 1µm and a concentration of 80 g/l via the left ventricle of the heart of mice under anesthesia using a peristaltic pump. The mice contained C51 or U87 tumors grown during two to three weeks until they clearly emerged to be easily extracted post mortem. The tumors were transferred to Eppendorf tubes filled with 4% para-formealdehyde for fixation. For the tomography measurements at the beamline TOMCAT (SLS at PSI, Switzerland) using the photon energy of 18 keV (bandwidth 2% to 3%) the container was fixed on the high- precision manipulator that rotated the tumor from 0^◦ to 180^◦ in steps of 0.12^◦ to record 1501 projections. It should be mentioned that continuous irradiation of the specimen caused the formation of bubbles. To master this serious problem, the shutter in front of the specimen was closed during CCD-readout. Hence, the irradiation could be interrupted by 0.1 s between the exposure periods of 0.3 s per projection. The conventional filtered back-projection algorithm

served for the reconstruction. Because the specimen was significantly larger than the field of view, local tomography of the inner part was performed, which yielded relative local X-ray absorption coefficients. The 3D representations of the vessel morphology were generated by means of VG Studio MAX 1.2.1 (Volume Graphics, Heidelberg, Germany).

20 µm

a) b)

Figure 2.1: The 3D representation shows the stained vessels. The yellow-colored arrow denotes an about 20 µm-wide vessel. The red-colored arrow indicates a barium sulfate accumulation associated with the contrast agent as the result of a damaged vessel wall. b) The 3D image demonstrates that many capillaries in the tumor exhibit a spiral shape as exemplarily indicated by the yellow-colored arrow.

2.3 Results and Discussion

The homogeneous staining of the capillaries using barium sulfate micro- and nanometer sized particles is demanding, since the carrier medium has to exhibit low viscosity that associates with density differences to the barium sulfate. Consequently, sedimentation phenomena can- not be avoided, which result in an inhomogeneous sulfate particle distribution of the vessel trees [11, 17]. The smaller vessels often appear interrupted [17]. In order to improve the sit- uation, the suspension should be suitably selected. The sedimentation velocity used, derived from Stokes law, should be as small as possible. It depends on the particle’s grain radiusr_p, the density difference between the carrier medium and the particles ρ−ρp, the viscosity of the fluidη and the gravitation constant g:

v_sed = 2 9

(ρ−ρ_p)·r_p²·g

η (2.1)

The most important parameter is the barium sulfate particle size. It has not only to be smaller than the smallest capillary, but well below one micrometer to reach low enough sedimentation velocities. Much smaller nanometer-sized particles, however, show a strong tendency to form clusters, which stop the perfusion through the blood vessel tree. Accordingly, globular barium

sulfate particles with a narrow sub-micrometer size distribution provide most homogeneous vessel staining. Healthy and cancerous tissue can be straightforwardly differentiated, since the fast grown tumor tissue exhibits a much higher density of capillaries than the surround- ing healthy vascular structure. In several regions, however, the opposite behavior has been observed [21]. The explanation lies most probably in the necrosis of the inner part of the tumor. It is hypothesized that the path from the arteries to the veins within the necrotic part of the tumor is not intact anymore. Furthermore, there are several indications for damages of the vessel walls. First, already in alive mouse the tumor becomes dark red in the advanced stages indicating extended regions of blood coagulation. Second, the applied pressure for the injection of the barium sulfate suspension generates leakage as experimentally found at several sites of the tumor tissue [21] and demonstrated in Figure 2.1(a). Nevertheless, blood vessels in the cancerous tissue with diameters down to 11µm could be clearly identified. The morphology of the vessel tree and the related shape of individual vessels within the cancer- ous tissue significantly differ from the healthy parts. The 3D representation in Figure 2.1 b) demonstrates that many vessels show a spiral shape, which belongs to typical signs of can- cer tissue [50]. These details cannot be identified usingin vivo magnetic resonance imaging, where only vessels with diameters down to about 80 µm come to light. The quantitative analysis of the barium sulfate stained vessels of the tumor, however, remains questionable, since significant parts are not stained and parameters such as the bifurcation probability versus vessel diameter cannot be meaningfully extracted. Therefore, the value of our study for the validation of computer simulations on the tumor formation [7] is limited. Here, it is highly desirable to improve the spatial resolution of phase contrast techniques that usually offer enough contrast to visualize the vessel tree without any stain even in para-formaldehyde solution [21].

Chapter 3

Global and Local Hard X-ray

Tomography of a Centimeter-sized Tumor Vessel Tree

3.1 Introduction

Cancer is a leading cause of death worldwide [2]. Many studies in cancer research investigate the neo-vascularization in cancerous tissue to get insight in tumor formation and growth [21]

with the aim to develop strategies against the disease. For the detailed investigation of the underlying phenomena, a three-dimensional visualization of the tumor vessel tree down to the capillary level would be most helpful. The smallest capillaries in the tumors (of centimeter size) have a diameter of around 4 µm and a wall thickness of about 1 µm [24, 51]. Syn- chrotron radiation-based micro computed tomography (SRµCT) reaches the sub-micrometer regime without X-ray optics [52, 53], but for the given resolution the field of view (FOV) is restricted. For specimens, which exceed the FOV, one can only cut the specimen into pieces of appropriate size or use the stitching technique where the projections are recorded at different asymmetric rotation axes to obtain the entire projection images of the tumor for each rotation angle [19, 53]. These techniques are time-consuming because they require the acquisition of many more detector frames than a standard tomography scan. Moreover, the volume of the data tends to become huge, which results in long times needed for data reconstruction, and difficult management of the data. Consequently, many research teams only acquire a region of interest (ROI) of the entire projection and reconstruct just these partial datasets, an approach known as local tomography or truncated-projection tomography. In local tomography, how- ever, the reconstructed X-ray absorption coefficientsµ(x,y,z) do not correspond to the values obtained from globally acquired data [28,53–55]. The deviations, a result of the interior prob- lem, can only be slightly evaded [28] but not completely corrected [56]. Different algorithms have been reported to partially correct the related artifacts [57, 58]. For cases in which the absorption coefficients are known a priori for a subset of the ROI to be reconstructed, the problem can be solved, but this requires iterative algorithms, which are relatively complex and computationally intensive [59]. The present work deals with the question how far the local X-ray absorption coefficientsµ(x,y,z) in the different local tomograms can be corrected using the information from the less detailed global data. First, it is tried to shift and scale

the binnedµ-values of the local data to obtain the ones of the global tomogram. Second, the artifacts in the local tomogram have been reduced combining the high-resolution projections with less detailed data of the missing regions before reconstruction. Third, using the rigid or affine registration the influence of distortions for example as the result of the objective’s aberration is addressed. Hence, the pros and cons of local tomography and the combination between local and global tomography are elucidated. It should be noted that the corrosion cast of the tumor vessel tree is especially suitable for this kind of evaluation as only two com- ponents (polymer and air) are present and, therefore, the density resolution is not a limiting factor.

3.2 Methods and Materials

3.2.1 Specimen Preparation

Three balb/c nude mice (Charles River Laboratories, France) have been used for the experi- ments in strict adherence to the Swiss law from animal protection. A suspension of 106 C51 tumor cells (murine colon carcinoma) was injected subcutaneously on the left flank of each animal. Ten days following injection, when the tumor have reached an average diameter of about 10 mm, mice were sacrificed and perfused with a polyurethane-based material [25] in order to produce a corrosion cast of the whole circulatory system. The casted tumor were subsequently extracted and treated with OsO4to enhance the contrast in SRµCT. The tumor cast was fixed on the sample holder with wax, as shown in Figure 3.1.

Wax Tumour cast

Figure 3.1: The photograph shows the corrosion cast of C51 tumor vessels grown in nude mouse. The black color of the polyurethane cast results from the OsO4 treatment. Wax served for fixation on the rotation stage for data acquisition.

3.2.2 Synchrotron Radiation-based Micro Computed Tomography

SRµCT measurements were performed at the TOMCAT beamline (Swiss Light Source SLS, Paul Scherrer Institute, Villigen, Switzerland) in absorption contrast mode [60]. A double multilayer monochromator was used to select a photon energy of 15 keV. The tumor cast was fixed on the rotation stage to acquire 1500 projections in 0.12^◦ steps between 0 and 180^◦. The high-resolution imaging detector is based on a 4.2-megapixel CCD camera (PCO [61], Germany, 2048 × 2048 pixels; 7.4 µm physical pixel size) coupled to the X-ray beam by a microscope lens system (Optique Peter, Lyon, France) and a 20µm-thin single-crystal scintil- lator made of cerium-doped lutetium aluminum garnet (LAG:Ce) which converted the X-rays into visible light. The microscope objective determines the magnification and the actual effec- tive pixel size on the specimen scale. In this experiment, a PLAPO1.25×(numerical aperture (NA) 0.04) and a UPLAPO10× (NA 0.4) objective from the Olympus UIS series (Olympus Corporation, Tokyo, Japan) were used. Tomograms of the whole specimen were measured using the 1.25x objective; the effective nominal pixel size with this objective was 5.92 µm.

The field of view of 12 mm for this setup was sufficient to enclose the maximal diameter of the tumor. But the pixel size was too large to discriminate between tiny capillaries and to extract their diameters. Six hours after the global measurements the setup is changed to 10x objec- tive, which leads to a lateral dimension of 0.74µm for each detector pixel The resulting FOV, however, is only 1.5 mm wide, which is substantially smaller than the tumor size. Therefore, this objective was only applied to perform local tomography. For both settings an exposure time of 0.175 s per radiograph was used. The global and local measurements were carried out each within approximately five minutes. The distance between the specimen and scintil- lator was estimated to 2 mm for global and local data acquisition. This short distance was chosen to minimize the effect of edge-enhancing propagation-based phase contrast, although this phenomenon cannot be completely eliminated. At the X-ray wavelength of 0.83 ˚A, the characteristic width of phase-contrast fringes at this propagation distance is (2 mm x 0.83

˚A)^0.5 = 0.4µm. In the reconstructed tomograms, this leads to bright/dark fringe pairs, which broaden the histograms of the absorption coefficients. The distance between the camera and the scintillator was 30 cm whereby the scintillator to objective distance was 2 to 3 mm for the 0.04 objective lens and several 100µm for the 0.4 objective lens.

3.2.3 Data Analysis Flat-field Correction

Flat-field images were taken before and after the acquisition of the projection radiographs in each tomography scan. The mean intensity of the flat-field images taken before data acquisition was higher by 7.2% for the global and by 2.0% for the local datasets than the ones recorded after data acquisition. This can only partly be explained by variations of the electron beam current in the source, because the top-up mode operation of the SLS keeps these variations to approx. 2%. The reason could be the darkening of the detector lens optics and/or predominantly, thermal changes of the monochromator. In the radiographs measured with a pixel size of 5.92µm there are areas without X-ray absorbing specimen, which allows extracting the time dependent decay of intensity. This information was implemented into the flat-field correction of the radiographs. For the flat-field correction of the data acquired with a pixel size of 0.74 µm, the background images taken before and after the projection

radiographs were interpolated linearly before flat-field normalization.

Reconstruction

The tomographic reconstruction of both the global and the local tomography datasets was performed using the filtered back-projection technique, implemented in the parallel-beam reconstruction software PyHST (European Synchrotron Radiation Facility, Grenoble, France) [62].

Projection Analysis

The global and local projections were compared to determine potential differences between the two objectives. The projections were termed global for 5.92 µm pixel size and local for 0.74µm pixel size. For comparison the corresponding ROIs in the global and local projections were selected. Rigid registration based on similarity transform was carried out (see Figure 3.2) to identify the same ROIs (common volume) in both images [63]. The software used for the registration was MATLAB R2010a and Simulink (Mathworks Inc., Natwick, MA, U.S.A.).

The similarity transformation in two dimensions includes the two translation parameters (tx, t_y), uniform scaling (s) and one rotation parameter (ϕ).

x⁰ y⁰

scosϕ −ssinϕ ssinϕ scosϕ

x y

+

t_x t_y

(3.1) The coordinates x⁰ and y⁰ describe the transformed coordinates. The registration process implies that one image (floating image) is transformed according to the reference image until optimal similarity is achieved for the similarity function. Here, the ’Normalized Mutual Information’ (NMI) was used as similarity function, which allows the registration of images with different intensity distributions [64]. To obtain the NMI, first the joint histogramh(a, b) of the two images had to be determined. The components consist of the X-ray absorption coefficients from local image (a) and the absorption coefficients from the global image (b).

The intensity values in the joint histogram correspond to the counts of the absorption-value combinations in the local and the global image, respectively. The values of the joint histogram (a,b) describe the number of joint pixels between the reference and floating images. When creating a joint histogram of identical images all values lie on a diagonal through the origin.

From the joint histogram the probability density functionp(a, b) can be determined:

p(a, b) = 1

Nh(a, b) (3.2)

whereN is the number of values in the joint histogram. p(a, b) describes the probability that two pixels in the reference and floating images with the same coordinate have the intensity valuesaand b. Using p(a, b) the Shannon-Wiener entropy Hab could be determined:

H_ab=−X

p(a, b) log (p(a, b)) (3.3) The higher the similarity between two images, the lower is the Shannon-Wiener entropy. The NMIY_abis determined using the Shannon-Wiener entropy. The advantage of the NMI against the entropy is that it does not simply maximize the overlap of air.

Y_ab = H_a+H_b Hab

(3.4) The NMI maximizes at the optimal alignment and can be thought of as a measure of how well one image explains the other. For the preparation of the projections for the registration a region, which is seen in the global as well as in the local projections is manually cropped.

The cropped region was defined to be the floating image. The reference image here was the local projection, which had been binned by a factor of eight, the nearest integer value to the scaling parameter, to obtain approximately the same number of pixels in both datasets. After registration the rotation and translation parameters were used to refine the cropping. The scaling parameter was applied to refine the re-sample factor for re-sizing the local projection.

Re-scaling was achieved by 2D cubic convolution interpolation of the image. The registra- tion was repeated using the optimized floating and reference images until maximal similarity between the images were achieved. A histogram was calculated from the cropped global and the re-scaled local projections to compare the intensity distribution of both images.

Tumor Analysis

Analogue to the projections, a three-dimensional (3D) registration tool [46] to register the tomography data was applied. The transformations were carried out along the x-, y- and z- axes so one obtained the translation parameters (t_x,t_y,t_z). The scaling depends here on three orthogonal directions. Hence, the three scaling parameters s_x, s_y, and s_z were introduced.

The histograms of the cropped global and the re-sampled local 3D datasets were determined.

Histogram Analysis

Histograms characterize the contrast and density resolution of tomography data [65]. Here, the peak positions and the related full-width-at-half-maximum (FWHM) values were determined.

The histograms of the global and local tomograms were compared.

3.3 Results

3.3.1 Differences between Global and Local Radiographs

Figure 3.3 (a) shows a characteristic global radiograph (pixel size 5.92 µm). The dashed rectangle represents the region used for local tomography. The full-line rectangle indicates the selected ROI. The radiographs depicted in Figure 3.3 (b) to (e) correspond to this ROI and contain grids as guidelines. The radiograph in Figure 3.3 (b) corresponds to the local projection (pixel size 0.74 µm). The related down-sampled radiograph using a factor of 8.11 is shown in Figure 3.3 (d). The factor 8.11 originates from the scaling of the rigid registration with the global data. Figure 3.3 (c) is the cropped part of the global projection as given in the full-line rectangle. The image in Figure 3.3 (e) shows the difference image between the global and the down-sampled local projection. In order to get a more detailed understanding of the differences between global and local radiographs, their histograms and selected line profiles are displayed in Figure 3.4. The histograms and line profiles originate from the data shown in Figure 3.3 (c) and (d). The locations of the profiles are denoted using the dashed lines in

θ_max = θ_Global

Crop ROI in global image using t_x, t_y ϕ = 0, s = 8

Roughly estimated t_x, t_y

Re-sample local image using s

Find new ϕ,t_x, t_y, s with rigid registration of global (θ_Global) and local (θLocal) images using similarity transform to maximaize NMI

Crop ROI in global image using t_x, t_y

Re-sample localimage using s Rotate global image using ϕ

Calculate NMI₁

θGlobal > θLocal + 10 ? θ_Global=θ_Global+1

|NMI₀−NMI₁|<ε?

true false

false NMI₀ = NMI1

true Calculate NMI₀

NMI_max = 0 θ_Global = θ_Local-10

NMI₁ > NMI_max ? true ^θmax = θ_Global

false

use θ_max

Figure 3.2: The registration procedure of local and global data is summarized in the flow diagram. θ describes the rotation angle step at which the projection was scanned. The local projections serve as reference the global projections as floating image.

(d) (e)

0

(c)

0.5 400 µm

(a)

0 0.6 1.2

Frequency [a.u.]

-log(I/I0)

(b)

-log(I/I0)

-log(Il/Ig)

0.5 10.5

Figure 3.3: The radiographs of the tumor vessel cast were measured at TOMCAT beamline (SLS at Paul Scherrer Institute, Villigen, Switzerland): (a) global radiograph with a pixel size of 5.92µm; dashed rectangle illustrates the region measured for local tomography with a pixel size of 0.74 µm; full line rectangle denotes the region-of-interest shown in the other images:

(b) radiograph of local tomography using a pixel size of 0.74µm, (c) cropped area from global radiograph, (d) re-sampled image from local radiograph; (e) difference image between the (I_g) and re-sampled local (Il) projection to reveal intensity differences. The 100 µm grids are incorporated as guidelines.

Figure 3.3. Both diagrams confirm the 35% higherI/I0-range in intensity for the local data.

As expected, the profile of the local projection shows more details.

-0.5 0.5 1.5 2.5

200 1000 1800

Frequency [a.u.]

150 300 450

0.2 0.6 1.0 1.4

-log(I/I0)

-log(I/I₀)

Position [µm]

(a)

(b)

Global

Local (re-sampled)

Figure 3.4: (a) The histograms of the global radiographs (blue-colored full line) and of the local radiographs (red-colored dashed line) are obtained from the ROI in Figure 3. (b) The line profiles denoted by the dashed lines in Figure 3 also show that the dynamic range of the local radiographs is by about 30% larger with respect to the global data.

3.3.2 Analysis of the Flat-field Images

The flat-field images (see Figure 3.5) show the typical stripes that come from the multilayer monochromator [20]. The signal intensity in these raw data describes the number of X-ray photons which have been converted into visible light and recorded by the CCD camera. The entity in which the signal is measured is called analogue-to-digital unit (ADU). The signal is much lower in the global image (Figure 3.5 (a)) than in the local image (Figure 3.5 (b)). The flat-field image in Figure 3.5 (b) is down-sampled using the factor of 8.11 to obtain the same number of pixels in the two images. The vertical profiles along the dashed lines in the images show the quantification of the observed intensity differences and are shown as examples in Figure 3.5 (c). The related histograms of the 2D images shown in Figure 3.5 (d) differ in peak position by 34% and in FWHM by 75%. The incident photon flux and exposure times per detector frame and the CCD as well as the scintillator used for both measurements were identical, so that the differences must be attributed to the detector lens optics. Indeed, these

differences can be quantitatively explained from the different magnifications and numerical apertures of the microscope objectives used (see below) and should be fully eliminated as the result of flat-field corrections. The ADUs of the re-sampled local flat-field image shows visible over-saturation by 9.3%. The maximal ADU value in the non-re-sampled local flat-field image is 0.5% below the saturation limit.

3.3.3 The Absorption Histograms of Global and Local Tomography Slices Figure 3.6 (a) shows a selected slice of global tomography from the tumor cast. The dashed circle encloses an area imaged in local tomography. The local region has been found in the global tomograms by 3D registration. The area within the square is presented in image of Figure 3.6 (c) as cropped, in the image of Figure 3.6 (d) as local tomography slice re- sampled prior reconstruction using the scaling factor of 8.11, and in the image of Figure 3.6 (e) as high-resolution local tomography slice. The incorporated grids validate the appropriate registration. The differences between the images are properly reflected by the histograms in Figure 3.6 (b). The histogram of the local tomography slices is remarkably broader than that of the global data. Even more important, there are substantial shifts of the peak positions to higher X-ray absorption coefficients.

Comparing the two histograms of local tomography one recognizes that the re-sampling has caused a 57% reduction of the FWHM of the air peak close to µ = 0. Such a reduction is the result of the large re-sampling factor and the associated binning [65]. The second peak located between 10 and 20 cm-1 originates from the Os-loaded polyurethane. There is a third peak above 60 cm-1 (not shown in Figure 3.6 (b), see Table 3.1), which stems from remaining bone (also Os-loaded) and relates to the bright clusters in the tomography slices.

3.3.4 The Absorption Histograms of Global and Local Tomograms

Figure 3.7 compares the absorption histograms of the 3D datasets. Figure 3.7 (a) shows the effect of re-sampling using the scaling factor 8.11. As already recognized for the 2D data the re-sampling gives rise to significantly sharper peaks. It is reasonable to analyze the effect of local reconstruction in absence of the differences in the optics. This can be achieved by truncating the ROI from the global projections before reconstruction is carried out. In Figure 3.7 (b) the histograms of the globally acquired images, where ROI cropping took place after (blue-colored, full line) and before (red-colored, dashed line) reconstruction, are shown. The locally reconstructed data are slightly shifted to higher absorption coefficients and exhibit significant peak broadening. Nevertheless, peak shift and broadening are much less pronounced than for the locally acquired data.

3.3.5 Correcting Local Tomograms using Histogram Matching

Local tomography does often not provide the correct local X-ray absorption coefficients, cp.

Figure 3.7. Therefore, the application of histogram matching well known from image process- ing to adjust the histograms of two images [66] might be an appropriate approach to correct the local X-ray absorption coefficients. In order to keep the procedure simple, the tomograms were directly modified instead of the radiographs. However, it was chosen to use a simplified approximation to histogram matching that uses only two scalar parameters and approximates the two histograms by stretching and shifting one of them. As shown in Figure 3.4 (a), the

200 µm

(a) (b)

Position [µm]

S0 [ADU]

Frequency [a.u.] S0 [ADU]

3 4 5 6 7 x 10⁴

1 2 3 4

0 500 1000 1500

3 4 5 6 7

Global

Local (re-sampled) Local

(d) x 10⁴ (c)

Figure 3.5: The flat-field images with low-magnifying objective, pixel size 5.92 µm and high- magnifying objective, pixel size 8.11 × 0.74 µm reveal an intensity radio according to the numerical apertures by 0.7 which is close to the expected value 66/100.

500 µm (a)

(c) (d) (e)

µ [1/cm]

Frequency [a.u.]

-10 0 10 20

10⁴

Global

Local (re-sampled) Local

(b)

10²

10⁰

Figure 3.6: The tomography slice (a) is globally acquired and shows a virtual cut through the entire tumor. The dashed circle encloses the locally acquired tomogram. The full line rectangle corresponds to the cropped area (c) the tomography slice of the local tomography, re-sampled using the factor 8.11 (d) and with the high spatial resolution (e). The related histograms of the slices (b) show the massive influence of the different analytical methods on the local X-ray absorption coefficients.

0 40 80 120 10⁰

10² 10⁴ 10⁶

Frequency [a.u.]

µ [1/cm]

10¹ 10

3 10

5 10⁷

Frequency [a.u.]

Global

Truncated local Local

Local (re-sampled) (a)

(b)

Figure 3.7: The diagrams show the histograms of the 3D data: (a) the influence of re-sampling the local data using the factor 8.11; (b) cropping globally acquired data before and after re- construction - red-colored dashed and blue-colored full line, respectively. Three peaks can be identified in the 3D histograms which are related to air, polymer and bone for increasing order.

histograms of the radiographs exhibit just one peak of different FWHM. To equate the FWHM of the re-sampled local data to that of the global histogram, the intensity values for every lo- cally acquired and re-sampled radiographI(x, y) is corrected using the difference between the most frequently occurring intensity value in the global projection and in the local projection D, and the ratio of the FWHMsR:

IHM(x, y) =R[I(x, y)−1]−D (3.5) Based on the corrected radiographs IHM(x, y), tomograms were reconstructed and their his- tograms compared with the histograms of the original datasets. As displayed in Figure 3.8, this histogram matching procedure of the locally acquired data causes a significant peak sharpening and peak shifts to more reliable absorption coefficients. The sharpening in the histograms of the radiographs by 35% reduces the FWHM of the air peak by 25% for the local, re-sampled tomogram and 33% for the local tomogram. Nonetheless, the air-related peak in the corrected histograms is still well above zero.

10⁰ 10² 10⁴ 10⁶

Frequency [a.u.]

0 40 80 120

10⁴ 10⁷

µ [1/cm]

Frequency [a.u.]

Local Local

(histogram matched) (b)

Local (re-sampled &

histogram matched) Local (re-sampled) (a)

Global

Figure 3.8: Correcting local radiographs using histogram matching: (a) histograms of re- sampled tomography data and (b) histogram of high-resolution tomography data.

3.3.6 Extending Local Sinograms by Less Detailed Global Data

In order to complete the local projections, one may take advantage of the less detailed global projections. Because the local and global projections have different pixel sizes, the local projections were down-sampled using the factor of 8.11. The regions in the global projections showing the identical regions visible in the local ones were replaced by the down-sampled local projections with a precision in pixel size of 5.92µm. Figure 3.9 (a) shows the comparison of the histograms of the tomography data with and without such an extension. The extensions of the re-sampled local projections by the less detailed global ones lead to a slight shift to smaller absorption coefficients. Alternatively, one can up-sample the global projections to fit the pixel size of the local data. This approach, however, yields huge datasets. Figure 3.9 (b), therefore, shows the histograms of only one tomography slice. Again, the extension slightly shifts the peaks to more reasonable X-ray absorption coefficients. Unfortunately, it coincides with a significant broadening of the peaks.

0 40 80 120

10¹ 10³ 10

µ [1/cm]

Frequency [a.u.]

10² 10⁴ 10⁶

Frequency [a.u.]

(a)

Local (re-sampled &

region enhanced) Local (re-sampled)

Local Local

(region enhanced) (b)

5

Global

Global

Figure 3.9: Extending local sinograms by less detailed global data: (a) histogram of re-sampled tomography data and (b) histograms of high-resolution tomography data.

3.3.7 Empirical Cupping Correction

Cupping artifacts occur in cone-beam CT and result from beam hardening [1]. Although the origin of beam hardening is quite different, similar behavior could be identified in the